# Geometric Mean Calculator

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Instructions:
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Use this Geometric Mean Calculator to enter the sample data below and the solver will provide step-by-step calculation of the geometric mean.

## More About this Geometric Mean Calculator

First of all, the geometric mean is a measure of central tendency, but it is a type of a less commonly used measure of central tendency, much less common than the sample mean or the median .

### How do you calculate the geometric mean?

The geometric mean is somewhat more cumbersome to calculate than it is to calculate the arithmetic mean. Mathematically, tn terms of its calculation, and the formula used to calculate it, it is computed by using the following formula

\[G = \left( x_1 \cdot x_2 \cdot \cdot \cdot x_n \right)^{1/n}\]In general, for the sample \(\{x_1, x_2, ..., x_n\}\), the arithmetic mean is larger than the geometric mean.

So, how to find geometric mean? Simply you multiply the n terms in the sample and apply the n-th root to that product. Simple.

### Applications of the Geometric Mean

There are different types of applications in which the geometric mean is the appropriate measure of center, or some other cases where the harmonic mean is the appropriate measure of center.

Still, by far, in the majority of applications, the arithmetic mean is the one that is used as measure of center, although is not unusual to find special situations.